Question: Rewrite as a simplified fraction. ${1.\overline{62} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 162.6262...\\ 1x &= 1.6262...\end{align*}}$ Subtracting the two equations, we have: ${99x = 161}$ ${x = \dfrac{161}{99}} \text{or} {1 \dfrac{62}{99}}$